Exporting ONLY the selected, visible faces of a scene
If trees are particle instances you will have to make them real first...



than delete all unwanted meshes in object mode to make first clean up, than select all (the rest of objects you want to export and if there is a lot of unwanted faces Join all objects (Ctrl+J), because like now, trees objects shares same object data (that can't be edited separately). If you are able to simply go to edit mode, select faces and delete - great, you can stop here and export. 

If you have some large faces out of your range you can cut them. Like ...

Go to Top View, create a new plane object on top of all objects, in size of area you want to export.



Select new plane first, than your joined object, switch to edit mode and search for Knife Project ...



in operator panel set Cut through



Select (B) the rest of vertices you want to keep ...

 

... invert selection (Ctrl+i) and delete.



Export result



but ... for a huge forest scene it can be killing process :)